H. Nyquist has shown that the rate of transmission through an ideal low-pass network cannot exceed two data pulses per hertz of passband, and that this theoretical limit can be approached by a transmission channel whose overall behaviour for data pulses is analogous to that of a gradual cut-off low-pass filter having a linear phase characteristic. That is why when seeking to provide data transmission at a high binary rate, one is constrained firstly to reduce the speed of transmission by replacing, for transmission purposes, binary data by multi-value symbols, and secondly to bring the characteristics of the link used by the transmission close to those of a gradual cut-off low-pass filter having a linear phase characteristic by such means as a shaping filter, modulation if so required, and correction of the distortion applied to the useful band by the link as set up for transmission.
The possibilities for correcting the distortion applied to the useful band by the link as set up for transmission depend on whether or not modulation has been used, and on the manner in which the binary data are replaced by multi-value symbols.
If there is no modulation, the correction is performed on the multi-value symbol. Whereas if there is modulation, the correction may be performed either before demodulation on the signal received from the transmission channel, or else after demodulation on the received mutli-value symbols.
The binary data train to be transmitted is replaced either by a single string of real multi-value symbols sent at a lower rate, or by a string of pairs of real multi-value symbols sent at a lower rate and transmitted simultaneously via two independent channels in quadrature. The first option is to be found in particular in base band transmission systems or in systems which use single, or residual, sideband amplitude modulation, the second option is to be found in data transmission using amplitude modulation of two carriers in guadrature or similar systems such as four or eight state phase-jump transmission or combined phase and amplitude modulation. When correction is performed on the received symbols, it is performed, as the case may be, on one channel or on two parallel channels which were transmitted in quadrature. Given the use of two channels in quadrature, it is possible to reduce the second option to the first by considering each pair of real symbols to be the real and the imaginary parts of a single complex symbol, and by replacing real values in the first option calculations by complex values.
The distortion occurring in the useful band is constituted firstly by slowing varying amplitude distortion and group propagation delay distortion of the transmission channel, and secondly by more rapidly varying phase noise.
The amplitude and group propagation delay distortion of the transmission channel is corrected by means of a filter whose characteristics in the useful band are the inverse of those of the transmission channel, whereby an overall flat response in the useful band is obtained both for amplitude and for phase linearity. It is known to use self-adaptive linear equalizers for this purpose, the basic structure of the equalizers being a time-domain transversal filter as described by K. E. Kalmann, with coefficients being varied in such a manner as to minimize the error between the received symbols and their exact values or their estimated values. Such equalizers adapt automatically to the characteristics of a transmission channel during a learning period during which the data train is replaced by a test sequence known at the receiver end, and thereafter adaptation continues throughout data transmission in response to the slow variations in the characteristics of the transmission channel.
One particular self-adaptive linear equalizer of the type mentioned above, and used to process a single channel, (after demodulation if required) comprises a time-domain transversal filter whose multiply-tapped delay line has a unit time interval equal to the period separating two symbols at the transmitter end, and whose coefficients are adapted constantly by feed-back control loops tending to minimize the mean square error by a gradient algorithm defined by a linear equation of first order differences between real magnitudes.
The above-mentioned self-adaptive linear equalizer, originally intended for a single channel, has a complex version for use with two channels in quadrature. This complex version can be deduced by using the "complex/real" correspondance mentioned earlier, and may be decomposed into four time-domain transversal filters disposed in a trellis configuration, having the same sets of co-efficients in pairs and whose outputs are interconnected in pairs, one pair via a subtractor and the other via an adder. The feed-back loops which tend to minimize the mean-square error employ a gradient algorithm defined by the same linear equation of first order differences, but this time between complex magnitudes.
This complex version of the above-mentioned self-adaptive linear equalizer is also used for processing a single channel instead of using the version based on one transversal filter. To do this, the single channel is associated with a quadrature channel to which there is applied the Hilbert transform of the signal from the single channel.
The relative amplitude of phase noise increases with transmission rate. The level of phase noise on the telephone network is acceptable for conversation or for low rates of data transmission (1,200 bits/s), but it becomes problematic for data transmission at a high rate (9,600 bits/s). It may include the following diverse components:
frequency drift, stemming, for example, from modulation followed by demodulation using un-synchronized carriers;
a constant phase shift;
a periodic phase shift varying at mains frequency or at one of its harmonics, which is to be found in particular when using carrier cables; and
a random phase shift at low frequency with respect to the bandwidth of the channel.
The phase noise can be considered as stemming from variations in the characteristics of the transmission channel. However, except for its DC and very low frequency components, phase noise cannot be eliminated by the linear self-adaptive equalizers used to correct amplitude and group propagation delay distortion in the transmission channel since they converge too slowly. Indeed, the above correction requires self-adaptive equalizers having a long impulse response with respect to that of the transmission channel which, taking the speed of transmission into account, requires the use of many coefficients. Now for stability reasons, the speed of a convergence of a linear self-adaptive equalizer is slower the larger the number of coefficients, and to a first approximation it is inversely proportional to the number of coefficients. For this reason, eliminating phase noise and more generally distortion attributable to rapid variation in the transmission channel must be done by means of additional correction circuits.
For example, at the receiver it is known to dispose a short, single coefficient linear self-adaptive equalizer between a long linear self-adaptive equalizer and a decision circuit which supplies an estimate of the transmitted symbols. It is also known at the receiver end of a digital data transmission system using amplitude modulation of two carriers in quadrature to dispose after the demodulator, a long self-adaptive linear equalizer followed by a self-adaptive complex phase shifter, the phase shift angle being adjusted in such a manner as to minimize the mean square error at its output using an algorithm defined, like that of the equalizer, by a linear equation of first order differences between complex magnitudes.
Both these arrangements are unsatisfactory since, in practice, frequency drifts are encountered which the additional correction circuits are incapable of following. Thus, improvements to the said arrangements have already been proposed; firstly by adding circuits for multiplying the coefficients of the long linear self-adaptive equalizer by the coefficient of the short self-adaptive equalizer in order to limit the amplitude of the corrections required of the short equalizer, however, this requires a large number of calculations to be performed; and secondly by disposing a second self-adaptive complex phase shifter in front of the long self-adaptive complex linear equalizer, likewise provided with a first order phase feed-back loop and having a phase shift angle adjusted to minimize the mean square error at its output, however, the improvement achieved is not sufficient, in particular when there is a large frequency drift.
The aim of the present invention is an improved correction of phase noise, and particularly that due to frequency drift, thereby improving the quality or the rate of a synchronous data transmission through a noisy medium such as the switched telephone network.